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43 Cards in this Set
- Front
- Back
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in terms of sine and cosine, tan = ______
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sin
____ cos |
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In terms of sine and cosine, csc = _____
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1
____ sin |
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In terms of sine and cosine, cot = _____
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cos
____ sin |
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In terms of sine and cosine, sec = _____
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1
____ cos |
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What are three pythagorean identities
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sin2x+cos2x=1
tan2x+1=sec2x 1+cot2x=csc2x |
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cofunction identity for cos?
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sin((pi/2)-u)=cos u
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cofunction identity for cot?
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tan((pi/2)-u)= cot u
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cofunction identity for csc?
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sec((pi/2)-u)=csc u
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cofunction identity for sin?
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cos((pi/2)-u)=sin u
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cofunction identity for tan?
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cot((pi/2)-u)= tan u
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cofunciton identity for sec?
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csc((pi/2)-u)=sec u
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3 even-odd identities
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sin(-x)=-sin x
cos(-x)=cos x tan(-x)=-tan x |
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Addition and subtraction formulas for sine?
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sin(s+t)=sin s cos t+cos s sin t
sin(s-t)=sin s cos t - cos s sin t |
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Addition and subtraction formulas for cosine?
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cos(s+t)=cos s cos t - sin s sin t
cos(s-t)=cos s cos t + sin s sin t |
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Addition and subtraction formulas for tangent?
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tan(s+t)= tan s + tan t
_____________ 1-tan s tan t tan (s-t)= tan s - tan t _____________ 1+tan s tan t |
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0 radians = ___ degrees
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0
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pi/6 radians = _____ degrees
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30
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pi/3 radians= ____ degrees
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60
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pi/2 radians= ____ degrees
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90
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pi/4 radians = ____ degrees
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45
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cos and sine for 0 radians
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1,0
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cos and sine for pi/6 radians
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sq(3)/2, 1/2
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cos and sine for pi/4 radians
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sq(2)/2
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cos and sine for pi/2 radians
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0,-1
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What is double angle formula for sine
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sin 2x= 2 sin x cos x
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What are 3 double angle formulas for cosine
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cos 2x= cos^2x-sin^2x
=1-2sin^2x =2cos^2x-1 |
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what is double angle formula for tangent
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tan2x= 2 tan x
_________ 1-tan^2x |
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name the sine sum-to-product formula when there is addition
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sin x + sin y= 2sin(x+y)/2 cos(x-y)/2
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name sum-to-product formula for sine when subtraction is used
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sin x-sin y= 2 cos(x+y)/2 sin(x-y)/2
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name sum-to-product formula for cosine when addition is used
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cos x+cos y=2cos(x+y)/2 cos(x-y)/2
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name sum-to-product formula for cos when subtraction is needed
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cos x-cos y= -2sin(x+y)/2 sin(x-y)/2
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what is product to sum formula for (sin u)(cos v)
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1/2[sin(u+v)+sin(u-v)]
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what is product to sum formula for] (cos u)(sin v)
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1/2[sin(u+v)-sin(u-v)]
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what is product to sum formula for (cos u)(cos v)
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1/2[cos(u+v)+cos(u-v)]
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what is product to sum formula for (sin u)(sin v)
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1/2[cos(u-v)-cos(u+v)]
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2 formulas for lowering powers for sin
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sin^2x=1-cos2x
_______ 2 sin x=sq(1-cos^2x) |
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what is half angle formula for sin?
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sin(u/2)=+-sq((1-cos u)/2)
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what is half angle formula for cos
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cos(u/2)=+-sq((1+cos u)/2)
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what are two half angle formulas for tan
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tan(u/2)=(1-cos u)/sin u
OR sin u/(1+cos u) |
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how do you decide whether to use + or - in sin and cos half angle formulas
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depends on which quad in which u/2 lies
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what is double angle formula for sine?
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sin 2x=(2sinx)(cosx)
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what are three double angle formulas fo cosine
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cos 2x= cos^2x-sin^2x
1-2sin^x 2cos^2x-1 |
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What is double angle formula for tangent
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tan 2x= 2 tan x
_______ 1-tan^2x |
